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In this paper, we compare two of the main paradigms of portfolio theory: mean variance analysis and expected utility. In particular, we show empirically that mean variance efficient portfolios are typically sub-optimal for non satiable and risk averse investors. We illustrate that the second order stochastic dominance (SSD) efficient set is the solution of a multi-objective optimization problem. We further show that the market portfolio is not necessarily a solution to this optimization problem. We also conduct an empirical analysis, examining the ex ante and ex post performance of SSD and mean variance efficient portfolios, using a bootstrap approach. In an ex ante analysis, we compare empirical moments, the level of diversification and set distances of mean variance and SSD efficient sets. We also show that the global minimum variance (GMV) portfolio and the part of the mean variance efficient frontier (MVEF) composed of highly diversified portfolios is second order stochastically dominated. This result also provides a possible alternative explanation for the diversification puzzle. Conducting an ex post analysis, we construct second order stochastic dominating strategies that outperform the GMV portfolio in terms of wealth and various other performance measures, producing a positive ex post opportunity cost.

This chapter mathematically derives the theoretical ZCAPM. To do this, we employ the geometry of the mean-variance investment parabola to show that a new CAPM (dubbed the ZCAPM) can be developed as a special case of Black’s (1972) zero-beta CAPM. As discussed in the previous chapter, Black’s zero-beta CAPM posits that an infinite number of pairs of efficient index I and orthogonal inefficient ZI portfolios on the investment parabola are possible. Each pair of portfolios can be used to proxy the market portfolio M. Here we show that the ZCAPM is based on two orthogonal portfolios denoted \(I^*\) and \(ZI^*\) on the parabola that have the same variance of returns. Given these two unique portfolios, we utilize random matrix theory mathematics to derive expressions for their expected returns. The resultant ZCAPM is an alternative but equivalent form of Black’s zero-beta CAPM. Unlike other CAPM models, the market factors in the ZCAPM can be readily estimated using daily market returns for assets. In applications to stocks (for example), the ZCAPM requires only the mean and cross-sectional standard deviation (return dispersion) of daily returns for all stocks in the market. These values can be easily computed. In the ZCAPM, sensitivities of an individual stock or portfolio to average stock market returns and market return dispersion are measures of beta risk and zeta risk, respectively. Unlike other models that incorporate return dispersion as an asset pricing factor, zeta risk captures both positive and negative sensitivity to return dispersion on any day t. These contrary forces of cross-sectional market volatility risk are a distinctive feature of the ZCAPM due to its close connection to the mean-variance investment parabola. In our theoretical derivation of the ZCAPM, we rely heavily on Markowitz’s (1959) mean-variance investment parabola and Black’s (1972) zero-beta CAPM, which itself is a more general form of the Sharpe’s (1964) CAPM. Hence, our ZCAPM stands on the shoulders of these classical finance theories by famous authors that were awarded the Nobel Prize in Economics. In this regard, we are most indebted to Fischer Black, who passed away before receiving Nobel recognition. We duly, albeit posthumously, celebrate his valuable insights that made possible our ZCAPM.

Some scholars, represented by William F. Sharpe and John Lintner, have established the "Capital Asset Pricing Model" (CAPM) in the 1960s. This model finds that under certain assumptions the expected rate of return shows a clear linear relationship with market risk (systemic risk), no matter for a single asset or a combined asset. Capital Asset Pricing Model (CAPM), is regarded as the spine of modern price theory in financial market. It has been applied widely to asset pricing analysis and determination, such as stocks, funds and bonds and to investment decision field. This essay based on CSMAR data, separately uses CAPM and the Fama-French Three-Factor Model to conduct empirical test on the expected return of SSE A-share portfolio. The main conclusion is that in China’s stock market, market risk is not the only factor which determines the expected return of the market portfolio or individual stock, while the size factor (SMB) and book-to-market ratio factor (HML) can better explain the portfolio’s expected rate of return.

In this paper, we aim to model the impact of the presence of socially responsible investors on asset pricing. We predict that the presence of ethical investors leads to partially segmented markets, and thus market portfolio inefficiency. Indeed, if some investors do not want to hold some assets because of their ethical preferences, the other investors, which want to invest in all assets, need to take into account total risk instead of market risk, because a part of the idiosyncratic risk is no more diversifiable. We demonstrate that an unpleasant consequence of SRI is that since investors refuse to hold all assets because of ethical considerations, “unethical” firms must be priced lower than other firms, to compensate conventional investors for not being able to hold the market portfolio.

Overall level of export fluctuations of the export-oriented countries with rising export volume partly stem from the market failure caused by free choice of export enterprises, some government intervention thus may be necessary. To reduce the level of fluctuations of the export growth rates in these countries, this paper, taking the significant differences of the exports among various markets into account and thus using a new index named relative variance to measure the export volatility risks, proposes a model of merchandise market portfolio, a modified version of Markowitz model, available to provide explicit guidelines for the firms, the industries and even the whole country to optimize the structure of their export markets. An application of this model to the case of China's apple is then discussed. The results show that the market share of China’s apple in 7 sub-markets should be redistributed drastically.

A plethora of research exists on the Capital Asset Pricing Model and how to tackle the unobservability of the true market portfolio. We contribute to this debate by providing an overview of commonly used proxies for the market portfolio embedded into a critical evaluation of these proxies. In particular, we evaluate equal- and value-weighted equity market proxies, a multi-asset approach, and a macroeconomic method. Since all proxies have strengths and weaknesses, we propose doing a case-by-case evaluation to reconcile the underlying goal of the analysis with the choice of the appropriate market proxy. A plethora of research exists on the Capital Asset Pricing Model and how to tackle the unobservability of the true market portfolio. We contribute to this debate by providing an overview of commonly used proxies for the market portfolio embedded into a critical evaluation of these proxies. In particular, we evaluate equal- and value-weighted equity market proxies, a multi-asset approach, and a macroeconomic method. Since all proxies have strengths and weaknesses, we propose doing a case-by-case evaluation to reconcile the underlying goal of the analysis with the choice of the appropriate market proxy.

We highlight the role of entropy maximization in several fundamental results in financial mathematics. They are the two fund theorem for Markowitz efficient portfolios, the existence and uniqueness of a market portfolio in the capital asset pricing model, the fundamental theorem of asset pricing, the selection of a martingale measure for pricing contingent claims in an incomplete market and the calculation of super/sub-hedging bounds and portfolios. The connection of diverse important results in finance with the method of entropy maximization indicates the significant influence of methodology of physical science in financial research.

We provide robust evidence that the price of analysts' dispersion risk in the cross-section of stock returns changes sign over time, and in particular, turns positive (negative) in periods of high (low) analysts' dispersion. Our result holds for a set of portfolios that are double-sorted on their betas and their coefficients on aggregate dispersion, as well as 36 different sets of test portfolios created by Kenneth French. We construct a general equilibrium model in which analysts of different types have heterogeneous beliefs about aggregate earnings growth. The consumer does not trust either analyst fully, and dynamically adjusts the weight given to each analyst, given the history of their past forecast performance. In equilibrium, each asset's risk premium depends on its exposure to three factors: (i) the market portfolio, (ii) the macroeconomic factor, and, (iii) a ``flight-to-safety'' factor. The first term decreases with dispersion, while the third term increases. These changes occurs because investors shift into assets with lower cash flow betas during periods of high dispersion. We find strong support for such a flight-to-safety in the data.

We analyze portfolios constructed from the principal eigenvector of the equity returns' correlation matrix and compare how well these portfolios track the capitalization weighted market portfolio. It is well known empirically that principal eigenportfolios are a good proxy for the market portfolio. We quantify this property through the large-dimensional asymptotic analysis of a spike model, which is comprised of a rank-1 matrix and a random matrix. We show that, in this limit, the top eigenvector of the correlation matrix is close to the vector of market betas divided component-wise by returns standard deviation. Historical returns data supports this analytical explanation for the correspondence between the top eigenportfolio and the market portfolio. We further examine this correspondence using eigenvectors obtained from hierarchically constructed tensors where stocks are separated into their respective industry sectors. This hierarchical approach provides robustness in eigenportfolio construction for a large number of equity returns when a shortened time window is used. For portfolios constructed using a rolling window of only one month of daily returns, our study shows improved tracking between the returns of the market portfolio and those from hierarchically constructed portfolios.

While there may be debates about passive and active investing, and even blogs about the numbers of active funds that were outperformed by the market, the history taught us that the outperformance of active or passive investing is cyclical. As a proxy for the active investing, the paper examines factor strategies and their smart allocation using fast or slow time-series momentum signals, the relative weights based on the strength of the signals and even blending the signals. While the performance can be significantly improved, using those smart approaches, the factors still got beaten by the market in both US and EAFE sample. However, the passive approach did not show to be superior. The factor strategies and market are significantly negatively correlated and impressively complement each other. The combined Smart Factors and market portfolio vastly outperforms both factors and market throughout the sample in both markets. With the combined approach, the ever-present market falls can be at least mitigated or profitable thanks to the factors.

We find that a large portion of U.S. equity mutual funds almost second-order stochastically dominates the market portfolio. Consistent with the canonical definition of second-order stochastic dominance, both fund investors and managers reveal their preference for funds with a higher degree of almost second-order stochastic dominance through higher inflows and higher manager ownership. Funds with a higher degree of stochastic dominance over the market portfolio significantly outperform their peers, after controlling for common performance predictors and the Sharpe ratio. Inference based on stochastic dominance is more consistent with the Manipulation-Proof Performance Measure (MPPM) than with the Sharpe ratio.

International financial markets are increasingly becoming integrated, especially in developed financial markets. This increased integration between financial markets is caused by increased globalisation and as a result, investors and portfolio managers are faced with numerous challenges when it comes to portfolio diversification of developed listed real estate markets. Literature indicates that investing in emerging financial markets as an alternative investment avenue may provide investors and portfolio managers with significant diversification benefits. Most of these studies were based on developed economies with the concentration on mixed asset portfolios and reflected limited research as this mainly focused on listed real estate only, with portfolios from the emerging financial markets.

In this chapter, a risk-free asset is added to the set of investable securities and the optimal portfolios are now derived in this augmented economy. One of the results obtained is that, in the risk/return analysis, the parameters (σ, m) of any investment portfolio lay either on or inside a certain cone \(\mathcal {C}(\sigma , m)\). The upper side of the cone represents the efficient investment portfolios and is called the Capital Market Line. We show that the portfolios on the Capital Market Line can be built as an allocation between the risk-free asset and a particular investment portfolio, made of risky assets only, called the Tangent Portfolio. The Tangent Portfolio appears to define the tangent point between the cone \(\mathcal {C}(\sigma , m)\) and the hyperbola \(\mathcal {F}(\sigma , m)\) delimiting the (σ, m) of all investment portfolios made of risky assets only. Based on some economic reasoning, the Tangent Portfolio is sometimes assimilated to the Market Portfolio, for which the investment in each asset is proportional to its relative market capitalisation. We also show in this chapter that the problem of optimal allocation can be segmented into two steps. First, the investor decides on the risk exposure he is ready to take, secondly, he calculates the allocation to the Tangent Portfolio which gives him this level of risk (the rest of the money being invested in the risk-free asset). This paradigm for investing is known as the Separation Theorem of James Tobin (Nobel Prize in Economics in 1981, see Tobin) and shows that whatever the risk appetite is, there is only one way to take risk exposure efficiently.

The derivation of observable implications of the conditional CAPM theory often includes the joint (internally inconsistent) hypothesis that the stock portfolio used in the tests is the theoretical, mean-variance efficient, market portfolio. The present paper generalizes this derivation by avoiding this joint hypothesis. The generalization reveals that the conditional CAPM plausibly explains asset pricing anomalies, such as the unconditional alphas and betas of momentum, value, and size portfolios, while the unconditional CAPM theory is still rejected by portfolios with negative unconditional betas and positive unconditional alphas. Hence, relaxing this joint assumption does not render the CAPM theory untestable.

Previous research finds that machine learning methods predict short-term return variation in the cross-section of stocks, even when these methods do not impose strict economic restrictions. However, without such restrictions, the models' predictions fail to generalize in a number of important ways, such as predicting time-series variation in returns to the market portfolio and long-short characteristic sorted portfolios. I show that this shortfall can be remedied by imposing restrictions, that reflect findings in the financial economics literature, in the architectural design of a neural network model and provide recommendations for using machine learning methods in asset pricing. Additionally, I study return predictability over multiple future horizons, thus shedding light on the dynamics of intermediate and long-run conditional expected returns.

A large literature is concerned with measuring economic uncertainty and quantifying its impact on real decisions, such as investment, hiring, and R&D, and ultimately economic growth. The COVID-19 pandemic underscores the importance of timely measures of uncertainty and expected growth across horizons. Asset prices, such as dividend futures and index options, provide particularly useful measures as they are forward looking and available at high frequencies. We extend this literature by using new data on the prices of options on index-level dividends, from which we can compute implied dividend volatility. These implied volatilities differ from the VIX which measures uncertainty about stock prices, not only uncertainty about dividends. We construct a term structure of implied dividend volatilities that characterizes how uncertainty varies across horizons. We study how this term structure developed over the COVID-19 crisis, documenting a substantial increase in the volatility of near-future dividends that lingers even as the volatility of the overall market portfolio has started to fall. In addition to introducing this market, we also provide new theoretical results that show how these data can be used to derive lower bounds on expected dividend returns and on expected growth rates, by maturity. This provides an alternative to methods used in the literature using vector autoregressions or survey expectations, and sharpens alternative bounds in the literature.

We use the staggered state-level stay-at-home orders in the U.S. as the difference-in-differences strategy to study the effect of remote work on the performance of actively managed equity mutual funds. After the implementation of working from home, fund daily returns over market returns decrease by 90 basis points per day, corresponding to a 6-million-dollar economic loss per day relative to investing in the market portfolio. Remote work also decreases measures of managerial skill, especially for funds not belonging to a family. These results suggest that working from home impairs mutual fund performance.

We investigate the added value of strategically allocating to the Chinese A-shares equity market. Our results indicate a positive contribution to a portfolio which only considers traditional developed and emerging equity markets and bonds. We find that a diversified A-shares portfolio based on value, quality, and momentum factors exhibits a significantly better risk-adjusted performance than the passive A-shares market portfolio. Consequently, allocating to Chinese A-share factor premiums significantly improves the efficient frontier. The conclusions remain similar when incorporating conservative estimates of trading costs or when constructing value-weighted portfolios, which represent more realistic investor returns.

Generous consideration has been pursued to the empirical testing of multi factor assets pricing models. However, literature provides mixed kind of evidences in the support of multi factor assets pricing model. This study reviews 20 research articles based on multi factor assets pricing model and examines 25 research papers based on the empirically testing of multi factor assets pricing model published during 2001 and 2018 to study the multi factor assets pricing model in the Indian context as well as foreign context. CAPM is a popular normative model used by researchers to explain the relationship between risk and expected return of a risky asset which was developed by Sharpe (1964) and Lintner (1965). This model takes only one risk factor which is the excess market portfolio return (Market premium). Because of poor performance of CAPM in explaining realized returns, the Fama and French three factor asset pricing model (1993) was developed. Fama and French (1993) documented the size effect and the value effect that were not included in the CAPM, generally known as CAPM anomalies. Mark M. Carhart (1997) developed the Carhart four factor model. It is an extension of the FF three factor model with one another factor i.e. momentum factor effect for asset pricing of stocks. In view of the limitations of the earlier three-factor model, Fama and French five-factor asset pricing model (2014) was developed. Fama and French (2014) came with profitability pattern and investment pattern in average stock return along with the market premium, size premium and value premium. This paper may be an expedient source of information to the academics, financial analyst and researchers to understand the asset pricing model.

Novy-Marx (2013, 2014) argues that profitability and value are philosophically and economically related: buying highly productive firms at average prices is similar to buying average productivity firms at low prices. We investigate the risk and return of portfolios that hold the entire market but tilt towards the joint distribution of stocks that rank highly on both value and profitability. Over 1940-2019, such “tilted market portfolios” generate substantially higher returns than the pure market portfolio. Even in periods where value has delivered weak returns (2000-2019), tilted market portfolios offer attractive risk-reward ratios. For investors with long horizons, bootstrapped simulations of up to 30-year holding periods indicate that the entire distribution shifts further to the right, generating better outcomes for investors. We conclude that benefits to long-only investors come from targeting value and profitability jointly, rather than running them side-by-side or sprinkling one with the other.

Martin (2017) and subsequent authors derive lower bounds for risk premia on the market portfolio and for individual stocks using option prices. If the bounds are tight and the options market is informationally efficient, then the bounds must be the best possible predictors of returns. We test the bounds conditionally and find that they are valid in all market conditions but are not tight in all market conditions. Slackness is significant and predictable. Adding predicted slackness to a bound produces a return predictor that is superior to using the bound alone.

Financial innovations in recent decades have vastly expanded investors' portfolio choice. We theoretically analyze the effect of these developments on investors' savings and asset returns. In our model, investors with possibly heterogeneous beliefs choose their savings portfolios. Under mild assumptions, we establish a choice channel by which greater portfolio choice increases investors' (perceived) return from saving, and induces them to save more. We then investigate the asset pricing implications of the choice channel, which depend on the type of financial innovation. Our main result shows that greater customization, which we capture with improved ability to trade risky assets other than the market portfolio, reduces the expected return on every asset. This result is consistent with the decline in the risk-free interest rate since the early 1980s, and is in contrast with the "precautionary savings" literature that would make the opposite prediction. Greater participation, which we capture with improved ability to trade the market portfolio, reduces the risk premia but typically increases the risk-free rate. We also analyze the effect of greater securitization, which we capture with a relaxation of constraints to issue risk-free promises in an environment in which there is a high demand for safe assets.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

We investigate risk and return in the major corporate bond markets of the developed world. We find that average returns increase with maturity and ratings class (where ratings go from high to low). From a pricing perspective, we find little to no evidence against the World CAPM model, where the market consists out of equity, sovereign and corporate bonds. However, from a factor model perspective a model, which separates the market portfolio into its three components, fits much more of the corporate bond return variation. In addition, local factors contribute substantially more to the variation of corporate bond returns than do global factors, and a \textquotedblleft local\textquotedblright\ three-factor model explains more than 80\% of the return variation for 59 of 63 portfolios examined. The factor exposures show intuitive patterns; for example as ratings worsen, equity $\beta$'s show a hockey stick pattern, sovereign $\beta$'s decline monotonically and the corporate bond $\beta$'s increase steeply. Our results are robust to the use of hedged versus unhedged returns and are also corroborated by a panel regression at the CUSIP level.

Using a newly constructed unique dataset, this study is the first to document returns of the market portfolio for a long period and with a high level of detail. Our market portfolio basically contains all assets in which financial investors have invested. We analyze nominal, real, and excess return and risk characteristics of this global multi-asset market portfolio and the asset categories over the period 1960 to 2015. The global market portfolio realizes a compounded real return of 4.38% with a standard deviation of 11.6% from 1960 until 2015. In the inflationary period from 1960 to 1979, the compounded real return of the GMP is 2.27%, while this is 5.57% in the disinflationary period from 1980 to 2015. The reward for the average investor is a compounded return of 3.24%-points above the saver’s. We also compare the performance of an investor who holds the market portfolio with an investor who uses simple heuristics for the portfolio allocation. Our results suggest that the market portfolio is close to the mean-variance frontier, but our heuristic allocations achieve a significantly higher reward for risk.

In this paper we present empirical tests of an extended version of the capital asset pricing model (CAPM) that replaces the single-period horizon with a probability distribution over different horizons. Adopting a simple parameterization of the probability distribution of the length of the horizon, we estimate the parameters of the distribution as well as the parameters of the CAPM. We find that the extended model is not rejected for several different samples of common stocks, and for these samples it outperforms not only the standard CAPM but also the Fama–French (1993) 3-factor model. The probability distribution over horizon dates varies over time with the New York Stock Exchange (NYSE) turnover rate. We also find that returns satisfy the Euler equation of a representative financial institution that holds the market portfolio and has horizon probabilities estimated from 13F filings.

Many photovoltaic and wind generation capacity owners gain access to power markets by signing up with virtual power plants. Power generation from these renewable sources of electricity is inherently uncertain and, consequently, revenue is random, which induces a risk for the owner. In this study, we investigate to what extent pooling different technologies and locations in the portfolio of a virtual power plant can reduce aggregate risk. To this end, we develop stochastic models for factors driving the assets’ underlying market and volume risks on which we base a model for risk-optimized pooling. Using the German market as an example, we demonstrate that optimal portfolios have a clearly better risk/return profile than the market portfolio. This finding holds in the case without subsidies as well as the case with feed-in tariffs.

Many studies have revealed that global financial markets are experiencing low-risk anomalies. In the Korean market, for example, even the portfolios of high-risk stocks recorded a loss of about 70% between 2000 and 2016. In this study, we construct a low-risk portfolio that responds to low-risk anomalies in the Korean market using the Black–Litterman framework. We use three machine-learning predictive and traditional time-series models to predict the volatility of assets listed in the Korean Stock Price Index 200 (KOSPI 200) and select the best-performing one. Then, we use the model to classify assets into high- and low-risk groups and create a Black–Litterman portfolio that reflects the investor's view where low-risk stocks outperform high-risk stocks. The experiment shows that reflecting the low-risk view in the market equilibrium portfolio improves profitability and that this view dominates the market portfolio.

We analyze the characteristics of 22 leading equity indices and discuss common biases relative to their respective national equity markets. Findings demonstrate systematic risk-factor exposures on a universally consistent basis in form of a large-cap, low beta, growth and contrarian tilt. These systematic biases are also relevant given their knock-on effect on public changes in consumption due to a changes in net wealth, especially as more private investors are utilizing ETFs on the basis of these indices rather than delegated mandates in form of mutual or pension funds.

Using the relation between the surprise component in labor statistics and an asset’s return on labor news announcement days, we derive a labor beta. By adding a labor news hedge portfolio which is long in high labor beta assets and short in low labor beta assets to the market portfolio, we obtain a labor news model. This model describes the cross-section of expected stock returns just as well as or even better than alternative multifactor models. The estimated premium for bearing labor income risk varies between three and five percentage points per annum.

In a panel survey of brokerage clients in the United Kingdom, participants mostly perceive their own portfolio as no more volatile than the market portfolio. Taking into account observed portfolio betas, this implies a belief in very low idiosyncratic portfolio volatility, which is even negative for a considerable fraction of the studied investor population. Possible explanations are extreme overconfidence in combination with a misunderstanding of how market and portfolio volatility are related. The identified bias contributes to underdiversification, as a belief in negative idiosyncratic volatility conceals the true benefits of diversification. In an experiment, we confirm the existence of a belief in negative volatility and rule out the underestimation of beta as an alternative explanation.

We propose an econometrically logical approach that distinguishes intentional from inadvertent smoothing of hedge fund return. Other than the hedge fund return (Y) we introduce an explanatory variable: a market portfolio of hedge fund returns (X). By connecting X and Y, some critical parameters are found to be effectively related to testing the two types of return smoothing. Using those parameters, we develop distinct desmoothing algorithms against intentional and inadvertent smoothing. Our empirical results show that although intentional smoothing is partly responsible for hedge fund smoothing and is done more consistently than inadvertent smoothing, return smoothing is mainly caused by the nature of underlying assets.

Thirty-five years after the World Market Wealth Portfolio of Ibbotson and Siegel [1983], this article summarizes the authors’ attempt to measure the stock of a broad universe of assets worldwide. Therefore, by measuring the global capital stock of assets (both financial and nonfinancial) in the economy, the authors intend to provide a proxy for the theoretical global market portfolio. The authors compute the market value of global assets included in 11 asset classes for the 2005–2016 period. Despite the limited availability of data for nonfinancial assets, the authors argue that their proxy for the global market portfolio is a much-needed starting point for those willing to diversify away from traditional domestic portfolios and achieve global asset class diversification.

In this paper, we have attempted to provide new evidence regarding American art as an investment vehicle, using tools typically employed to evaluate the investment worthiness of financial assets. We provided a brief review of the CAPM, and then estimated a general version of it allowing betas to differ between early American and contemporary American art using auction data on paired sales during the period 1987–2013. Our results indicate that early American art and contemporary American art are two distinct asset classes; that contemporary American art is probably a good investment on strictly financial grounds, but early American art may not be; that incorporating transactions costs is crucial to evaluating whether art is a good investment in some cases; that it is in principle possible to design an asset portfolio containing only American art that mimics the investment characteristics of the market portfolio; and that what appeared to be an art bubble bursting in the fall of 2015 may simply have been a predictable response of art prices to a drop in the stock market.

In this work, we apply the Modern Portfolio Theory and the Capital Assets Pricing Model financial tools to a portfolio of CO2-emitting generation technologies under diverse scenarios. We will calculate the efficient—in the sense of having the minimum risk for a given level of emissions—portfolios frontier. The Capital Market Line (CML) is the place where all the possible combinations of a specific efficient portfolio and a pollution-free portfolio—made up with nuclear and renewable generation technologies—lie. In Finance, that specific efficient portfolio is called the market portfolio but we will see that in our case it lacks an evident meaning. Therefore, we will explain which should be the reference portfolio for power generation planning analysis. Anyway, the fact is that those combinations are less pollutant than the portfolios in the efficient frontier. Thus, a policy-maker can analyse which is their effect on emissions reduction. We will start analysing the efficient pollutant generation portfolios. Then, we will introduce the CML-analogous lines (CML-A) to allow the possibility of reducing emissions by combining an efficient portfolio with a non-pollutant portfolio—this non-pollutant portfolio is free of both emissions and risk. Results support the necessity of considering the carbon capture and storage technology to achieve a less risky generation mix, with less emissions and allowing a higher diversification due to the presence of cleaner fossil fuel technologies. All of that leads to better levels of energy security.

Online promotion helps enhance brand awareness and boost sales. Although it attracts customer traffic, an ill-conceived price promotion has serious repercussions because it disproportionately draws bargain hunters, results in profit erosion and causes operational chaos due to erratic demands. This research proposes a long-term optimization model to help dual channel (click-and-mortar) retailers understand the conditions necessary to promote products online across all markets. When partial markets are recommended, we investigate how to price and select the market portfolio for promotion in each time period. We develop a multi-objective evolutionary algorithm to efficiently solve complex and large-scale problems. Both theoretical analysis and numerical study show that the proposed model outperforms the conventional strategy of promoting online across the board. Due to its dynamic nature, the multi-period recurring promotion problem is difficult to address optimally. Our model is capable of planning for multiple periods, multiple markets, and multiple objectives to maximize long term profitability and competitiveness. Click-and-mortar retailers will find our approach extremely effective for maximizing profit, enhancing brand awareness, and improving customer satisfaction.

Market portfolio composition substantially affects the cost of equity estimates. Adding Treasury securities to an equity‐only market portfolio substantially changes both estimated market betas and the estimated market excess return. Though the sign and magnitude of the net impact of these changes are uncertain, they dramatically impact costs of equity for 30 industry portfolios under the Capital Asset Pricing Model (CAPM) and Fama‐French (1993) Three‐Factor Model. The choice of market portfolio proxy is as important as the choice of the pricing model when estimating costs of equity. Similar conclusions hold when we add real estate, corporate debt, and international securities to the market portfolio.

Given a competitive equilibrium in complete asset markets, we propose a method that aggregates heterogeneous individual beliefs into a single “market probability,” which, if commonly shared by investors, generates the same marginal valuation of assets by the market as well as by each individual investor. As a result of the aggregation process, the market portfolio may have to be scalarly adjusted, upward or downward, a reflection of an aggregation bias due to the diversity of beliefs. From a dual viewpoint, the standard construction of an expected utility-maximizing aggregate investor designed to represent the economy in equilibrium, is shown to be also valid in the case of heterogeneous beliefs, modulo the above scalar adjustment of the market portfolio, thereby generating an Adjusted version of the Consumption based Capital Asset Pricing Model (ACCAPM). We analyze how the allocation of aggregate and individual risks relates to deviations of individual beliefs from the aggregate market probability. Finally, we identify the channels through which the distribution of beliefs and other microeconomic characteristics (incomes, attitudes toward risk) across investors impact the pricing of risky assets an may contribute to explaining the equity premium puzzle.

Accounting harmonization in Europe by International Financial Reporting Standard adoption is a recurrent object of study in the accounting literature. In this paper the consequences of the adoption of Standard-13 are analyzed. In particular, this research analyzes the effects on the implied volatility option (risk) for non-financial companies of three variables: financial leverage, own probability default (Debt Value Adjusted) and financial institutions credit risk (Credit Value Adjusted), before and after the adoption of the accounting standard on fair value. The empirical study focuses on member companies of the European Monetary Union zone to avoid other risk factors different to market risk (such as exchange rate or different risk free rate) and at the same time, easily identify the market portfolio (EUROSTOXX-50). To overcome the problems of endogeneity in the panel data, we use the technique System Generalized Method of Moments with instrumental variables to estimate the parameters. The results show that the leverage effect on excess risk does not change after adopting the Standard, however, its own and the financial institutions default probabilities become statistically significant. Furthermore, this novel methodology allows estimate industry asset betas and, in all cases the asset betas were lower than equity betas and, found an average debt beta of 0.4 for the sample period.

This paper establishes existence and uniqueness of equilibria in the capital asset pricing model ( CAPM ) in a setting with incomplete markets in which part of the endowments are non-tradeable. It is shown that in equilibrium, agents are willing to assume aggregate hedgeable risk of the market but will no longer hold fractions of the market portfolio. The paper studies the effects of non-traded endowments on equilibrium asset prices and allocations and establishes a linear pricing formula, a security market line, and conditions for the positivity of asset prices.

Minimum variance portfolio (MVP) seems to outperform the mean-variance optimized portfolio on a risk-adjusted basis. Scherer (2011) conjectures that the MVP tilts toward low beta and low idiosyncratic risk assets. Consequently, the MVP capitalizes on both the beta anomaly and the idiosyncratic risk anomaly. By providing a counter-example, Yanushevsky and Yanushevsky (2015) show that the proof of the conjecture is incomplete. In this article, we provide conditions under which Scherer (2011) conjecture remains valid. Specifically, we show that the counter-example in Yanushevsky and Yanushevsky (2015) represents a knife-edge case. We also analytically identify the MVP weight sign.

We investigate the size and value factors in the cross‐section of returns for the Chinese stock market. We find a significant size effect but no robust value effect. A zero‐cost small‐minus‐big (SMB) portfolio earns an average premium of 0.61% per month, which is statistically significant with a t‐value of 2.89 and economically important. In contrast, neither the market portfolio nor the zero‐cost high‐minus‐low (HML) portfolio has average premiums that are statistically different from zero. In both time‐series regressions and Fama–MacBeth cross‐sectional tests, SMB represents the strongest factor in explaining the cross‐section of Chinese stock returns. Our results contradict several existing studies which document a value effect. We show that this difference comes from the extreme values in a few months in the early years of the market with a small number of stocks and high volatility. Their impact becomes insignificant with a longer sample and proper volatility adjustment.

This study attempts to conduct a five-year performance assessment by analyzing all 24 closed-end mutual funds that had been trading at Dhaka Stock Exchange from December 2011 to January 2017. While analyzing the risk-return profile, the research incorporated both market price and net asset value (NAV) of the mutual funds.NAV depends on the price of securities included in a fund's portfolio whereas, the market price is determined by demand and supply forces. Thus, the market price of a fund is not always equal to its NAV. The study uses market price as a basis for analyzing the risk-return profile of the funds for evaluating the performance of the funds in the market. With the purpose of assessing the performance of asset managers, the study uses NAV as a basis for computing Jensen's α and M squared measure. While assessing performance the study focuses on Jensen’s α and M squared measure as other measures like Sharpe and Treynor do not work with negative numerators and do not provide information on whether the mutual fund outperformed the market portfolio. Both Jensen’s α and M squared measure can independently describe whether a fund beat the market or not. A positive value of Jensen’s α and M squared measure indicates that the fund outperformed the market considering respectively β and σ as a measure of risk. SEBL1STMF, POPULAR1MF, and IFILISLMF1 were among top four funds considering both M2 and Jensen’s alpha measures based on both market price and NAV. The M2 measure, a coefficient of variation, Sharpe ratio, and Treynor ranked SEBL1STMF as the best performer in the market. This fund also topped while assessing performance by M2 measure on the basis of NAV. On the basis of market price and NAV, 21 funds and 22 funds could produce positive M2 respectively. In the year 2012, 2013 and 2014 mutual funds provided negative annualized return on an average (On the basis of market price). The average annualized return rebounded on 2015 and further increased on 2016. All mutual funds provided a positive return in 2016. A different picture was found while calculating annualized return on the basis of NAV, asset managers could generate positive annualized returns on an average in 2013, 2014, 2015 and 2016.

We estimated the ex-ante equity risk premium for the Republic of Macedonia, which is a young, small and open emerging market. We polled academics and practitioners for their expectations on the stock market index MBI10 as a proxy for market portfolio. The risk premium is the expected MBI10 return relative to a government bond yield. Using the Kolmogorov–Smirnov and Anderson–Darling goodness-of-fit tests we determined the best fitted statistical distribution, and consequently estimated the short-term ERP of 8.55 and long-term average ERP for the next 10 years of 7.76. The estimated ex-ante ERP is higher and similar as it is in the other emerging markets. Key words: Emerging markets, Forecast, Market returns, Risk-free rate, Expected equity risk premium, Goodness-of-fit test.JEL: G11, G12, G14, G31. Ex-ante rizik premije kapitala: Ocekivanja na osnovu prognoza berzanskih premija na tržistu kapitala u razvoju Procenili smo ex-ante premiju rizika kapitala za Republiku Makedoniju, koja je mlado, malo i otvoreno tržiste u razvoju. Profesore i prakticare smo anketirali za ocekivanja u vezi indeksa MBI10 kao približnu varijablu za tržisni portfolio. Premija rizika je ocekivana vrednost povracaja MBI10 u odnosu na prinos državne obveznice. Koriscenjem testova adekvatnosti Kolmogorov-Smirnov i Anderson-Darling utvrdili smo najbolju statisticku raspodelu, a samim tim procenili kratkorocni ERP od 8.55 i dugorocni prosek ERP u narednih 10 godina od 7.76. Procenjeni ex-ante ERP je veci i slican kao sto je to na drugim tržistima u razvoju. Kljucne reci: Tržista u razvoju, predviđanje, povracaj na tržistu, stopa bez rizika, ocekivana premija rizika kapitala, test adekvatnosti.

We develop an efficient mixed-scale estimator for jump regressions using high-frequency asset returns. A fine time scale is used to accurately identify the locations of large rare jumps in the explanatory variables such as the price of the market portfolio. A coarse scale is then used in the estimation in order to attenuate the effect of trading frictions in the dependent variable such as the prices of potentially less liquid assets. The proposed estimator has a non-standard asymptotic distribution that cannot be made asymptotically pivotal via studentization. We propose a novel bootstrap procedure for feasible inference and justify its asymptotic validity. We show that the bootstrap provides an automatic higher-order asymptotic approximation by accounting for the sampling variation in estimates of nuisance quantities that are used in efficient estimation. The Monte Carlo analysis indicates good finite-sample performance of the general specification test and confidence intervals based on the bootstrap. We apply the method to a high-frequency panel of Dow stock prices together with the market index defined by the S&P 500 index futures over the period 2007–2014. We document remarkable temporal stability in the way that stocks react to market jumps. However, this relationship for many of the stocks in the sample is significantly noisier and more unstable during sector-specific jump events.

In this paper, we explore the impact of investor herding behavior on stock market volatility. We adopt a direct herding measure based on the variation of cross-sectional stock betas. The measure can be readily separated into positive and adverse components, whereby investors herd towards and away from the market portfolio, respectively. Using A-shares listed in the Chinese equity market from August 2005 to March 2021, we show that the market volatility is Granger caused by the measure, and that there exists an asymmetric effect between positive and adverse herding on volatility. Furthermore, we provide robust evidence that the information contained in the herding measure helps generate significantly improved volatility forecasts and add economic value to investors. Our paper not only contributes to the volatility forecasting literature but also advances our understanding of herding in the equity market.